Limita cu sume Riemann?
Posted: Sat Oct 11, 2008 6:15 pm
Fie \( a\in\mathbb{R} \) si sirul \( (x_{n})_{n\geq 1} \) dat de egalitatea
\( x_{n}=\sum_{k=0}^{n}\left(\frac{n^2+k}{n^2}\right)^{a}, \forall n\in\mathbb{N}^{*} \).
Sa se calculeze \( \lim_{n\to\infty}(x_{n}-n) \).
Gazeta Matematica seria B, 2001
\( x_{n}=\sum_{k=0}^{n}\left(\frac{n^2+k}{n^2}\right)^{a}, \forall n\in\mathbb{N}^{*} \).
Sa se calculeze \( \lim_{n\to\infty}(x_{n}-n) \).
Gazeta Matematica seria B, 2001